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Physics Letters B

Integrability for multidimensional lattice models

Jean Michel Maillet, Frank Willem Nijhoff

Published Jul 1, 1989• 74 citations
Publisher
DOI
10.1016/0370-2693(89)91466-4

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Modelling of Ultracold Gases in Multidimensional Optical Lattices

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Title: Modelling of Ultracold Gases in Multidimensional Optical Lattices Author: Miroslav Urbanek Department: Department of Chemical Physics and Optics Supervisor: doc. Ing. Pavel Soldán, Dr. Abstract: Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model. Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model. The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices. The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems. Keywords: Bose-Hubbard model, multidimensional system, optical lattice, tensor network

•Jan 1, 2017•0 citations
Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning.A fundamental problem in this area is the accurate evaluation of multidimensional integrals.An introduction to the theory of the stochastic optimal generating vectors has been given.A new optimized lattice sequence with a special choice of the optimal generating vector has been applied to compute multidimensional integrals up to 30-dimensions.Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.
Title: Modelling of Ultracold Gases in Multidimensional Optical Lattices Author: Miroslav Urbanek Department: Department of Chemical Physics and Optics Supervisor: doc. Ing. Pavel Soldán, Dr. Abstract: Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model. Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model. The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices. The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems. Keywords: Bose-Hubbard model, multidimensional system, optical lattice, tensor network